Wednesday, January 25, 2006

Disjunctive Requirements

You shouldn't believe contradictions. For any given proposition, you should disbelieve either it or its negation. This claim is ambiguous. It might mean the wide-scope disjunctive requirement:(WD) You ought to disbelieve either one of P or not-P (and it doesn't matter which, at least for the purposes of this requirement).Or it might instead be proposing a disjunction of narrow scope requirements:(ND) It is either the case that you ought to disbelieve P, or that you ought to disbelieve not-P.

For ND, it does matter which option you choose. One of them is the correct option, we just don't know which! WD, by contrast, can be satisfied equally well by either option. (Footnote 27 of Kolodny's 2005 illustrates this difference nicely. I can quote it if anyone wants further clarification.)

I find wide-scope requirements like WD interesting because, if normative, they open up a new aspect of (non-evidential) epistemic assessment. They might lead us to assess beliefs against internal standards of coherence and consistency, rather than the external standard of truth. I used this idea in an earlier essay to argue that there could be non-evidential reasons for belief: after all, even if there are no reasons at all to think that P is false, the mere fact that you believe not-P would seem to give you reason to disbelieve P, since doing so would bring you to satisfy requirement WD.

But I don't know how plausible that is. If all the evidence supports P, we might think it more plausible to simply insist that you ought to believe P, and - further - that there's nothing at all to be said in favour of disbelief, no matter that it contradicts your prior (ill-founded) belief that not-P. If you're more sympathetic to these claims, then you'll likely prefer ND to WD as the proper form of our non-contradiction rule.

Incidentally, this should not be confused with the simple narrow-scope conditional requirement:(NC) If you believe that P, then you are rationally required to disbelieve not-P.

NC is plainly false as a universal principle. Sometimes rationality requires us to reject our prior beliefs in favour of their negations. This lends support to the wide-scope reading of the conditional:(WC) Rationality requires that: if you believe that P, then you disbelieve not-P.

WC, unlike NC, may be satisfied by rejecting the antecedent (belief that P) as an alternative to fulfilling the consequent (disbelieving not-P). In fact, WC is logically equivalent to WD above (well, if we treat the earlier 'ought' as merely meaning "rationally required", leaving open the question of whether these requirements are genuinely normative). But this reminds us that there is a second way to revise NC. Rather than converting it into a wide-scope requirement, we might instead replace it with a disjunction of narrow-scope requirements, as in ND. So the problems with simple "NC"-style narrow-scope requirements need not lead us to accept wide-scope requirements.

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2 comments:

Maybe I'm just having a senior moment but I'm confused by all of that. Three basic questions:

1. How is WD different from ND or NC different from WC? It seems they are making exactly the same claim using different words.

2. Why is NC plainly false? If you reject your prior belief then there is no problem with NC because you no longer believe P. If you believe P and fail to disbelieve not-P you are being irrational regardless of whether P is actually true or whether you change your mind later.

3. When you say 'X disbelieves P', does that mean

a) X believes P is false; orb) X does not believe P is true

If the meaning is a) then WD and ND are false because it may be rational to form no belief about the truth of P, e.g. if P is 'there is currently an odd number of atoms in the universe'

If the meaning is b) then NC and WC are too weak because a belief in P rationally requires a positive belief that not-P is false.

Yeah, sorry, I should've been clearer. I was using 'disbelief' as short for "does not believe". That is, your option (b). "Weak" requirements are no problem, as they aren't claiming to exhaust our rational requirements. Perhaps there are other, stronger, requirements in addition to these weak ones. That's fine.

For your first question: the difference concerns the scope of the rational requirement. Let "RR(X)" denote "you are rationally required to X". Now, a wide-scope requirement takes the form "RR(A or B)", whereas the narrow scope disjunction is of the form "RR(A) or RR(B)".

Suppose I do B. Then I have definitely satisfied the wide-scope requirement, because all that requires is that I do either of A or B, and - here's the key point - it doesn't matter which one I do. I merely have to make sure I do any one of them. For example, to prove my identity I might have to show you either my passport or my drivers license, and it doesn't matter which one.

Now, the narrow scope case is different. Here it matters which one. It's either true that I'm required to do A, or else that I'm required to do B. We just don't know which one it is. If I did B, I'm not guaranteed to have satisfied this requirement. Perhaps I was instead required to do A. That is, perhaps RR(A) was the true disjunct, and not RR(B).

For example (to adapt Kolodny's illustration), I might not be sure which of two tax forms, A or B, I have to return. I'm definitely required to do one of them, but I'm just not sure which. This is not the same as being required to (return either one of A or B). For that wide-scope requirement, it doesn't matter which I do. I could satisfy it by returning form B. But let's suppose the law actually requires me to return form A (though I didn't know it). In that case, by returning form B I have not satisfied the legal requirement.

One final illustrative analogy: some people like sunshine, and some people like rain. This is a disjunction of narrow scope 'likings'. They're not both guaranteed to satisfy. (Perhaps I only like sunshine, and not rain.) Compare the wide-scope version: "I like days with sunshine or rain -- it doesn't matter which!". This wide-scope version is more lenient. It is similar to saying "I like both sunshine AND rain". This is quite different from the narrow-scope disjunctions mentioned above. They are harder to satisfy, because you might not know which one is right. For the wide-scope version, both options are "right" (or permissible).

Let me know if it's still unclear!

"Why is NC plainly false?"

NC allows for the following (unsound) argument:1. I believe P2. If I believe P then I'm rationally required to disbelieve not-P3. Thus, I'm rationally required to disbelieve not-P.

But 3 might not be true. Perhaps I'm instead rationally required to reject my belief that P, and start believing not-P. NC doesn't allow for this alternative option. That's why we need to change it to ND or WC/WD instead.

"If you reject your prior belief then there is no problem with NC because you no longer believe P."

NC is a problem for as long as you hold the prior belief, however. It doesn't properly allow for the possibility that we might be rationally required to reject it. It would lead to the (potentially) false conclusion that I'm rationally required to disbelieve not-P, when the very opposite might be true. I might be required to believe not-P. Because NC doesn't allow for this possibility, it must be false.

"If you believe P and fail to disbelieve not-P you are being irrational regardless..."

Yes, this is recognized by all the principles discussed in the post. But perhaps the problem is in the believing of P. NC doesn't allow for that. The others do.

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